Identification of commutative covariance structures by successive testing of statistical hypotheses

For the multidimensional stochastic systems obeying the regression models with unknown covariances of disturbances, consideration was given to the choice of a covariance model and estimation of its parameters. The invariant behavior of the regression model with the covariance matrix of a special structure was studied. In the problem of identifying the structure of a set of feasible covariance matrices, a procedure of successive testing of hypotheses was proposed. The unbiased and invariant uniformly optimal estimates of the parameters of the observation-based model were determined. The problem of identifying the model of covariances in experiment design with random factors was considered as an example.